试比较(3/4)^(-1/3)与(4/3)^(1/4)的大小.

问题描述:

试比较(3/4)^(-1/3)与(4/3)^(1/4)的大小.

(3/4)^(-1/3)
=(4/3)^(1/3)
(4/3)^(1/4)
4/3>1
1/3所以(3/4)^(-1/3)>4/3)^(1/4)

(3/4)^(-1/3)=(4/3)^(1/3)
(4/3)^(1/4)
因为底数为4/3>1
所以指数的图像为增函数,
因为1/3>1/4
所以
(4/3)^(1/3)>(4/3)^(1/4)

(3/4)^(-1/3)>(4/3)^(1/4)